Continental usually puts 2 small dimples in the tire tread to be used as wear indicators. When mine are almost gone, I'll take the tire off an use it indoors on a trainer only. I then move the front tire (which always lasts much longer) to the rear and put a NEW tire on the front. I like to keep the front as nice as possible since a blowout up there would be bad news.

As for running a tire until you see cords, that's up to you. Depends on your budget and how much risk you wanna take. Sometimes I end up 60 mi from home before I turn around, so I dont generally ride on tires that worn. For your short commute, that may be a totally acceptable way to go.